THE LAWS OF CONCENTRATED SOLUTIONS.
V.
68 I
that it would dissolve in the liquid, imparting to i t a yellow color. On the assumption that this observation, as well as the hypothesis just formulated is correct, the conclusion seems inevitable that a t temperatures below -60’ and unde’r the other conditions prevailing in the experiments, nascent nitrine, N,, is more active chemically than nascent chlorine. This may possibly be explained on the ground that the nascent chlorine tends a t once to polymerize into less active aggregates, while N, does not polymerize with equal readiness. Summary. In the present investigation it has been shown: ( I ) That solutions of ammonium trinitride in liquid ammonia readily conduct the current. (2) That with platinum electrodes of different sorts, under various conditions of concentration and of anode current density, electrolysis of the solutions results in the liberation of hydrogen a t the cathode, and of nitrogen (with negligible quantities of hydrogen) a t the anode, in a ratio H, : N, varying from 1.65 to 2.15 (and averaging 1.93),instead of the ratio 0.333 to be expected in case the discharged N,- ion simply breaks up into molecular nitrogen. (3) That these facts may be most readily explained by assuming that some of the N,- ions break up, after discharge, into molecular nitrogen, but that the greater number react with ammonia so as to regenerate ammonium trinitride and liberate (possibly nascent) nitrogen. (4) That with a graphite anode the ratio averages 0.334, indicating quantitative conversion of N, into molecular nitrogen. CORNELLUNIVERSITY, ITHACA, N. Y.
[CONTRIBUTION FROM THE LABORATORY OF PHYSICAL CHEMISTRY OF THE UNIVERSITY OF ILLINOIS. PUBLICATION No. 13.1
THE LAWS OF ‘‘CONCENTRATED” SOLUTIONS. V:l PART I: THE EQUILIBRIUM BETWEEN ARSENIOUS ACID AND IODINE IN AQUEOUS SOLUTION; PART 11: A GENERAL LAW FOR CHEMICAL EQUILIBRIUM IN SOLUTIONS CONTAINING IONS; PART 111: THE ENERGETICS OF THE REACTION BETWEEN ARSENIOUS ACID AND IODINE. B Y EDWARD w. WASHBURN A N D EARLBK.STRACHAN. Received March 29, 1913.
CONTENTS. I : I . Purpose of the Investigation. 2. Previous Investigations. 3. Outline of the Experimental Method. 4. Purification of Materials and Preparation of Solutions. j. The Distribution of Iodine between Water and Carbon Tetrachloride. The 4th paper of this series was published under the title, “The Electrical Conductance of Concentrated Solutions of Electrolytes,” Trans. Amer. Electrochem. SOC.,21, PART
125 (1912).
682
EDWARD W . WASHBURN A N D EARLE K . STRACHAN.
6 . The Conductance and Degree of Ionization of Hydriodic Acid. 7. The IodideTri-Iodide Equilibrium in Solutions of Hydriodic Acid. 8. The Ionization Constant of Arsenic Acid. 9. The Ionization Constants of Arsenious Acid. IO. Measurements of the Arsenious Acid-Iodine Equilibrium. I I . The Equilibrium Constant and the Mass Action Law. PART11: 1 2 . The Theoretical Interpretation of the Behavior of the Equilibrium with Respect to the Mass Action Law. 13. An Equation of State for Solutions Containing Ions. 14.A General Law for Chemical Equilibrium in Solutions Containing Ions. I j. Application of the General Law to the Ionization of a Uniunivalent Electrolyte. 16. Application of the General Law to the Reaction between Arsenious Acid and Iodine. PART111: 1 7 . The Heat of the Reaction. 18. The Free Energy of the Reaction. 19. The Potential of the Normal Arsenic Electrode. 20. Summary and Conclusions. PART I. THE EQUILIBRIUM BETWEEN ARSENIOUS ACID AND IODINE IN AQUEOUS SOLUTION. I . Purpose of the Investigation. When by dilution the mol fraction of the solute molecules in any solution becomes so small that the thermodynamic environmentz prevailing within the solution is substantially determined by the nature of the solvent molecules and is not appreciably affected by further dilution, then the solution may be classed as a “dilute” solution and will, within the experimental error, be governed by that set of limiting laws which are called, the Laws of Dilute Solutions. Solutions for which this condition is not fulfilled will exhibit deviations from these laws of magnitudes varying with the natures of the solute and solvent and with the degree of dilution. The development of a satisfactory theory for interpreting the behavior of this second class of solutions constitutes the problem of “concentrated” solutions in the sense in which the term is used in the title of this series of papers. The behavior of solutions of strong electrolytes in water indicates that the change of thermodynamic environment with changing concentration persists up to much higher dilutions than is the case with aqueous solutions of other solutes. In f a d , i t seems to persist up t? such high dilutions in many instances that, before a point is reached where it becomes approximately constant, the experimental errors in the data concerning the solutions have become so large that i t is no longer possible to draw trustworthy conclusions from them. This is illustrated, for example, by the familiar behavior of the strong electrolytes toward the law of mass action. With respect to this behavior, however, most of the attention in the past has been directed to the application of this law to the simple process of the dissociation of a strong electrolyte into its ions, and very little exact
The results of this investigation formed the subject of a Thesis submitted by Earle K. Strachan to the Graduate School of the University of Illinois in May, 1912,in partial fulfillment of the requirements for the dcgree of Doctor of Philosophy. This term was defined and discussed in No. IV of this series, loc czc. See also Trans. Amer. Electrochem. SOC., 2 2 , 331 (1912).
THE LAWS OF CONCENTRATED SOLUTIONS. V.
683
study has been made of other types of chemical reactions involving the ions of the strong electrolytes. The work which has been done in this field shows, it is true, that the other types of reactions thus far investigated do not exhibit the large deviatims from the law of mass action which characterize the simple ionization process, but the limits of error in most of the investigations thus far made, have been comparatively large and very decided deviations from the mass action law might still be present without being detected. As an example of this may be cited the work of Victor Sammet' which is one of the most thorough and accurate investigations of such a reaction that has been made. Sammet investigated the equilibrium of the reaction, 6H+ + 51IO,- = 31, 3H,O. He varied the concentrations of the different reacting substances through rather wide limits and was unable to find any evidence indicating a deviation from the law of mass action. For example, as the mean Qf one series of determinations of the equilibrium constant of this reaction, he found K = 0.26.10-~~ while another set yielded the value K = 0.46.10-*~. The second value is nearly double the first and individual experiments show even greater differences. As Sammet, himself, states,2 however, the agreement is as good as could be expected considering the uncertainty in the values of some of the auxiliary data employed in the calculation, and cannot be taken as indicating any real deviation from the requirements of the law of mass action. Another equilibrium of this character which has been investigated i s that between arsenious acid and iodine as expressed by the equation H3As03 1,- + H,O = H,AsO, 2H+ + SI-. This reaction has been studied by J. R. R o e b ~ c kbut , ~ the value of the equilibrium constant computed from his data is so uncertain, owing to the errors from various sources, that we can only conclude that at least no very great deviation from the law of mass action is indicated. Roebuck's experiments, however, showid that a definit equilibrium is quickly and easily reached and made it appear probable that the adoption of different experimental methods and the careful measurement of all the auxiliary data required would make it possible to compute the value of the equilibrium constant of this reaction with such a degree of accuracy that the total uncertainty in it, due to the combined effects of all the errors in the separate data required, would not exceed IO%. Any variation' from the requirements of the mass action law which exceeded this amount might, therefore, be detected.
+
+
+
+
Sammet, 2.physzk. Chem., ~3~ 656 (1905). LOC. Cd.,
*Roebuck, J . phys. Chem., 6 , 365
(1902);9,
727 (1905).
EDWARD W . WASHBURN AND EARLE K . STRACHAN.
684
In addition to the general theoretical interest attached to a more exact study of such a n equilibrium, this particular equilibrium is also interesting because of the fact that i t lies a t the foundation of what is perhaps the most accurate method of titrametric analysis known, the determination of iodine by titration with a standard solution of arsenious acid.‘ The development of this analytical method affords a striking example of the value of the ionic theory in the field of quantitative analysis, for i t is owing to this theory that i t was possible to secure that insight into the equilibria involved in the method which made it possible to recognize and to eliminate its sources of error and to predict those modifications which were necessary in order to give it the great exactness which it now possesses. By means of this method the atomic weight ratio, As,O,/I, and through it the atomic weight of arsenic could probably be determined with an accuracy of a few thausandths of one per cent. When employed in conjunction with the iodine coulometer the method, moreover, makes possible the determination of the exact value of the faraday with a degree of certainty unattained by any other coulometer.2 2 . Previous Investigations. In the investigation by J. R. Roebuck, referred to above, the following experimental method was employed : Measured quantities of standard solutions of sodium arsenite (As,O, dissolved in NaHCO,), iodine, potassium iodide, and sulfuric (or hydriodic) acid were mixed with water and allowed to come to equilibrium in a stoppered bottle at oo. When equilibrium was attained a sample was withdrawn, diluted with ice water in order to decrease the rate of reaction, and then the “free” iodine titrated with. standard thiosulfate solution. This titration was carried out as rapidly as possible, since the removal of the “free” iodine present disturbed the position of the equilibrium and caused an additional quantity to be formed. From these data a n equilibrium constant was calculated. The chief sources of error inherent in this experimental method are, as Roebuck, himself, points out; (I) The error due to the disturbance of the equilibrium in the process of determining its position, and (2) the formation of some “free” iodine by the action of dissolved oxygen according to the reaction, 0, + 4Hf 41- = 21, zH,O. Aside from the influences of these sources of error, the use of Roebuck’s data in order to calculate the true equilibrium constant of this reaction with any degree of certainty is rendered still more difficult by the fact that sodium and potassium salts, carbonates and bicarbonates, and in many experiments sulfuric acid also, were present in the equilibrium mixture. The presence of these additional substances greatly compli-
+
1 2
+
Washburn, THISJOURNAL, 30, 31 (1908). Washburn and Bates, THISJOURNAL, 34, 1341 (1912).
THE LAWS OF CONCENTRATED SOLUTIONS.
685
V.
cates the calculation of the concentrations of the molecular species directly concerned in the equilibrium itself and consequently introduces considerable uncertainty into the computation of the true equilibrium constant. Roebuck, in fact, made no attempt to compute the true equilibrium constant, but contented himself with expressing his results in a form equivalent to the following : [As’] [free acid I2[iodidel3 = const., [As][tri-iodide] where each quantity in brackets signifies the total concentration of the material indicated, in all the forms in which i t is present in the solution. Thus [As’] indicates [H3As04] [H,AsO,-] [NaH,AsO,] [KH,AsO,], and [tri-iodide] indicates [HI,] [I;] [NaI,] [KI,] [IJ, and similarly for the other substances involyed. The values of the “const.” thus calculated varied between the limits 1.03.IO-^ and 0.364. IO-^ in different experiments.’ An attempt to compute the true equilibrium constant from what seemed to be the most accurate as well as the simplest experiment carried out by Roebuck led to the value
+
+
+ +
+
+
+
With the exception of a n attempt by Loimnranta to measure directly the potential of the arsenic electrode, Roebuck’s investigation is the only study of this equilibrium which had been made when the present investigation was undertaken. Loimaranta’s experiments will be referred to below, section 19. 3. Outline of the Experimental Method. The sources of error and uncertainty described above can be avoided by employing the following procedure: A standard solution of pure arsenious acid dissolved in air-free water is allowed to react, out of contact with the air, with a second non-miscible phase containing a suitable quantity of pure iodine. The other substances concerned in the equilibrium should be insoluble in this second phase, which for convenience may be called the reference phase. Under these conditions the reaction which occurs may be writ ten H,AsO, 2H,O I, = H,AsO, 2H+ 21-. Immediately, however, the iodide ions produced react with more of the molecular iodine according to the reaction II, = 1,to give tri-iodide ions and when equilibrium is finally attained nearly a11 of the “free” (i. e., titratable) iodine present in the solution exists in the
+
+
+
+
LOC.ciL, Table XXXVIII, p. 763 of Roebuck’s second paper. Washburn, loc. cit., 34.
+
686
EDWARD W. WASHBURN AND EARLE K. STRACHAN.
form of tri-iodide. The equation for the equilibrium may, therefore, be conveniently written H,AsO, zH,O I; = H,AsO, zH' SI-. As will be shown later, when this equilibrium is attained, the solution contains, in addition to water, only the following ten molecular species a t appreciable concentrations : H,AsO,(or AsO.OH in acid solution), As0 +, H,AsO,, H,AsO,-, H+, I,, HI, HI,, I-, and I,-. Now if the total arsenic concentration, XAs gram atoms per liter, the total iodine concentration, XI gram atoms per liter, and the concentration of molecular iodine, [Ia], in the solution be determined, the concentration of each of the molecular species present can be computed in the following manner : AS] = [H,AsO,] [Asof] [H,AsO,] [H,AsO,-] (3) and [E11 = 2[&] [HI] [I-] 3[HI,I + 3[13-I (4) Moreover
+
+
+
+
+
+
+
+
+
+
and, as will be prpved below, hydriodic acid, HI, and hydrotriiodic acid, HI,, are ionized to the same degree, r. Hence by combining equations (4) and ( 5 ) we have I 3 [I21 [I-] [ZI] - 2[IJ = [I-] (6) r rkl The value of [I,], the concentration of molecular iodine in the solution, may be calculated from its concentration in the reference phase and the distribution ratio between the two phases. Equation (6) gives us, therefore, a t once the value of [I-]. The values of [HI], [HI,] and [I3-] can now be obtained from the equations,
+
[HI]
=
[I,-] I
[HI,]
e--
1-7 [I-1
(7)
r
LII-I k,
= ___
I-)= - [I,-
r
I.
(9)
Now as all the iodide, both ionized and unionized, results from the oxidation of arsenious acid, whereby for every molecule of arsenic acid formed, two molecules of hydriodic acid are obtained, and as all the triiodide results from the reaction, II, = 13-,it follows that the sum of all the molecules of hydriodic acid and of hydrotriiodic acid is twice the total number of molecules of arsenic acid, or (IO) 2[H,AsO,] 2[H2AsO4-] = [HI] [HI,] [I-] [I;].
+
+
+
+
+
THE CAWS OF CONCENTRATED SOLUTIONS.
V.
68 7
In order to obtain [H,AsO,], use is made of the ionization constant of arsenic acid,
the hydrogen ion concentration being obtained by a method of successive approximations to be explained below. The value of [H,AsO,] can be obtained from equation (3) together with the equilibrium relation
As the reference phase an excess of pure solid iodine was employed in t h e initial experiment. Under these conditions the value of [I,] in the solution is equal to the solubility of iodine in water. It was found, however, that when the equilibrium is established in the presence of an excess of iodine as a solid phase the reaction runs so far to the right that if the arsenious acid is to remain a t a measurable concentration, the hydrogen ion concentration will rise to about 0.2 normal, which is rather uqdesirable. I n order to avoid this and to make it possible to vary a t will the value of [Iz] in the solution, carbon tetrachloride was employed as the reference phase, preliminary experiments having shown that none of the other substances concerned in the equilibrium were appreciably soluble in this liquid. The calculation of the equilibrium constant from the data obtained by this method evidently requires the knowledge of a number of auxiliary d a t a in the way of equilibrium constants and degrees of ionization, several of which had to be especially determined for this investigation. After the methods of purification of materials and preparation of solutions have been given, the determination of these auxiliary data will be described, before the experiments dealing directly with the arsenious acid-iodine equilibrium itself are taken up. 4. Purification of Materials and Preparation of Stock Solutions. Arsenious Acid.-Kahlbaum’s Ph.G.IV, arsenic trioxide was crystallized once from hydrochloric acid and twice from conductivity water. After the first crystallization from water the substance went into solution completely, leaving no residue. The following method was used in making up the solution for the equilibrium determinations. The desired amount of Conductivity water was collected, boiling hot, from the still, and a t once sufficient arsenic trioxide to make a 0.05 molal solution was added to it. The water was then boiled until the arsenic trioxide had completely dissolved. While still hot the solution was transferred to a bottle of resist.ance glass. This bottle was fitted with a rubber stopper through which two glass tubes passed, one of them reaching just through the stopper, a n d the other to the bottom of the bottle. As soon as the solution had been
688
EDWARD W . WASHBURN AND EARLE K . STRACHAN.
introduced into the bottle, the longer tube was stopped and the shorter one connected to a supply of nitrogen gas. I n this way the solution was allowed to cool and was then preserved out of contact with the air. By attaching the short tube to the gasometer containing the nitrogen, opening the long tube, and increasing the pressure on the nitrogen, the arsenious acid could be forced out of the bottle in any amount desired. The exact strength of the solution was determined by titrating i t against pure iodine. Arsenic Acid.-This was prepared from the arsenic trioxide by evaporating i t to dryness with a large excess of aqua regia. The residue was then taken up in pure water and evaporated to dryness several times, and was finally dissolved in enough conductivity water to make a twice molal solution. The exact strength of the solution was determined by precipitating the arsenic as magnesium ammonium arsenate. lodine.-Kahlbaum’s resublimed iodine was ground with some potassium iodide and sublimed. The resulting product was then resublimed without the addition of potassium iodide. Hydriodic Acid-This was prepared by reduction of iodine with hydrogen sulfide, and subsequent distillation. After several distillations, the distillate was very pale yellow, and was free from sulfur. Carbon Tetrachloride.-Kahlbaum’s carbon tetrachloride was saturated with iodine and allowed to stand over night. The iodine was then removed by shaking with a solution of sodium thiosulfate, and the carbon tetrachloride washed several times with conductivity water. It was finally distilled in a current of nitrogen, and the distillate preserved under nitrogen. Nitrogen.-This was prepared by passing dry air over hot granulated copper. 5. The Distribution of Iodine between Water and Carbon Tetrachloride. Jakowkin’ has determined the partition constant for this distribution a t 2 5 O , and has found that i t decreases with decreasing concentration. For the purposes of this investigation, the partition constant must be known with a fair degree of accuracy, since an error in it of 1% causes a n error of 4% in the equilibrium constant. Jakowkin’s values, when plotted graphically (see figure) seem to indicate a decided increase in the partition constant a t the lowest concentration measured by him. This is not what would be expected from theory. Moreover, as his investigations were carried out a t considerably higher concentrations than those used in this work, it was thought desirable to make determinations of the partition constant a t the concentrations actually used. For this purpose, an accurately known weight of iodine was placed in a resistance-glass bottle together with an accurately known volume of water ( I O liters) and of carbon tetrachloride ( I liter). An amount of sulphuric Jakowkin, 2. physik. Chewt., 18,5 9 2 (1895).
THE LAWS OF CONCENTRATBD SOLUTIONS.
v.
689
acid (5 cc. of 1.84 sp. gr. acid) sufficient to prevent hydrolysis of the iodine, [HI01 [I-1I"[ = 0.3 X 1 0 - l ~ ~ was as calculated from the relation' --
[I, 1
for the ratio of the con- A centration of the iodineawin the carbon tetrachlo-
6. The Conductance and Degree of Ionization of Hydriodic Acid. T h e Conductance Data.-Ostwald2 has determined the conductances of aqueous solutions of hydriodic acid a t 2 5 O , but as the recent work of Bray and Hunt3 has shown that Ostwald's data for hydiochloric acid are in error by about 3%', i t was thought best to measure the conductances of hydriodic acid solutions a t those concentrations a t which i t occurred in the equilibrium mixtures. The solutions employed for this purpose were obtained from the stock solution by shaking it with pure benzene until a colorless solution was obtained. These solutions were then analyzed and they remained colorless until the conductance measurements were completed. The conductance cells and other apparatus employed in these measurements have been described in a previous publication' from this laboratory. The results obtained are recorded in Table I. Columns I and I1 give, respectively, Bray, THISJOURNAL, 32, 932 (1910). Ostwald, /. prukt. Chem., 32, 302 (1885). Bray and Hunt, THISJOURNAL,33,786 (1911). For example, these investigators give 390.4 as the equivalent conductance of 0.1normal HCI, while Ostwald found $8 I .o. ' Washburn and MacInnes, THISJOURNAL, 33, 1689 (1911).
690
EDWARD W. WASHBURN A N D
EARLE K ,
STRACHAN.
the concentrations given by analysis and the measured equivalent conductances. Columns I11 and IV give the corresponding values for round concentrations as determined by graphical interpolation. * TABLE~.--CONDUCTANCE I. C. 0.1710
0.1028 o ,09020 0.05I40
AND IONIZATION OF HI AT 25 O. CONCENTRATIONSIN LENTS PER LITER. I912 ATOMIC WEIGHTS. 11. 111. IV. V. A. C. A.
386.8 395.0 397.7 403.7
o.1goo 0.I o 0 0
0.0800 0.0500
389.5 395.6 398.5 404.3
EQIJIVAVI.
r.
Wb *
0.896 0.903 0.911 0.924
0.996 0.997 0.997 0.998
Calculation of y.-If A, is the equivalent conductance of the total iodide (both ionized and unionized) in any solution of'hydriodic acid and AI,- is the equivalent conductance of the iodide i o n in the same solution, then the degree of ionization y is given by the relation y = AI/At,-. Concerning the correctness of this relation there can, of course, be no question. The question arises when we consider the method to be employed in evaluating the two quantities A, and AII-. The first of these can in all probability be correctly calculated by means of the relation
A, = T,A (13) in which TI is the transference number of the iodide ion-constituent and A the equivalent conductance of the HI, both a t the concentration C. The correct method for calculating is less certain. The general question involved here has been discussed by one of the authors in the preceding number of this series,2 and will be more fully treated in a future publication. For the present we will simply state that the values of required for the purposes'of the present paper have been obtained by employing the relation All- = A,- (fife)" (14) in which AI- is the equivalent conductance of the iodide ion at zero concentration, (f/fo) is the relative fluidity of the hydriodic acid solution for which y is desired and m is the fluidity exponent for the iodide ion. Combining equations ( 1 3 ) and ( 1 4 ) with the relation y = AI/AtI-, we have finally for the degree of ionization of hydriodic acid
in which ( q / q o ) is the relative viscosity of the solution.
For the con-
Ostwald's values are considerably lower than these. Thus for 0.1normal HI he found A = 386. a LOC.cit., 133. In this article and in article number I1 of this series the evidence favoring the use of the relation A',- = AI- u/f0)"has been set forth. See also the where a different point of view recent paper by Lewis, THISJOURNAL, 34, 1637 (1912), is taken. 1
THE LAWS Or' CONCENTRATED SOLUTIONS.
V.
69 1
centration range involved in this investigation (0.05 to 0.I 5 N ) the value of TIis practically constant and equal to 0. I 74. The value of AI-a t 25 O is 76.5l and that of m is 0.8 but for the viscosities involved in this investigation may without appreciable error be taken as unity.2 Equation (IS) becomes therefore
Column V of Table I gives the values of j- calculated by means of this relation. The viscosity data given in column VI were determined in this laboratory by Mr. G. Y. Williams using the apparatus described below.S The values are so nearly equal to unity that the viscosity correction is practically negligible. 7. The Iodide-Triiodide Equilibrium in Solutions of Hydriodic Acid. The equilibrium constant, ['?'['-] ~
L-1
- k , , has been determined in a
number of ways by several different observers and the results of all these investigations have been recently subjected to a careful criticism by Bray and MacKay4 in connection with a further experimental study of this equilibrium. They found that in solutions of potassium iodide saturated with iodine the value of K , decreased from 1.53 to 1.31 between o and 0.1 normal KI, but that in a dilute potassium iodide solution lz, was practically constant with respect to variations in the concentration of 12. For the purposes of the present investigation it is necessary to know the value of k , quite accurately and to know how it behaves with respect to variations in the concentration of HI in the solution. I t seemed desirable, therefore, to determin the value of this constant in hydriodic acid solutions a t those concentrations actually employed in the experiments on the arsenious acidiodine equilibrium. By measuring the conductanaes of the solutions in these experiments, an opportunity would also be afforded for testing the assumption that H I and HI, are ionized to the same degree in solutions of the same total ion concentration. , The following experiments were accordingly made : Solutions of iodine in hydrodic acid of different concentrations were rotated in the thermostat a t 2 5 O in contact with a carbon tetrachloride layer until equilibrium was established. The two layers were then drawn off and analyzed. The I, in the carbon tetrachloride layer was determined by titration with standard thiosulfate and that in the water layer was calculated by means of the partition constant. A portion of the water layer was then shaken with successive portions of carbon tetrachloride until i t was colorless and a
Bray and MacKay, THISJOURNAL, 32, 921 (1910). Cf. equation 11, THISJOURNAL, 33, 1471 (1911). THISJOURNAL, 35, 737 (1913). Bray and hlacKay, THISJOURNAL, 32, 914 (1910).
EDWARD W. WASHBURN AND EARLS K. STRACHAN.
692
these carbon tetrachloride solutions were then titrated with the standard thiosulfate solution. In a second portion of the water layer the total iodine was then determined by Bray's permanganate method. TABLE II.-THE IODIDE-TRIIODIDE EQUILIBRIUM IN SOLUTIONS OF H I AT 25'. DATA AND RESULTS. CONCENTRATIONS, [ 1, I N FORMULA WGICHTS PER LITER. L . 108 [ZHII [I,] ~- k,. rHI
[XHI,I
I. 11. 111. IV. No. ["I]. 103. [ZHIa] . 103. [Id. 103. I 80.1 82.1 1.32 2 55.4 56.7 I .32 37.08 0.720 3 67.62 33.36 0.684 4 64.96 4.636 0.0694 5 87.62 0.0241 1.349 6 72.95 7 57.15 0.904 0.0202
+
HI^ =
[ZHI; 440
k l . 103.
VI. L . 106.
1.29 1.29 1.31 1.33 1.31 1.30 1.28
6195 4250 3973 3761 3652 2982 2342
V.
+ ["&I
VII.
rHI+HIa. 0.906 0.900 0.888
0.895 0.896 0.914 0.921
405
VIII. 2C;.
IX.
0.1471 O.IOO9 0.0930 0.0879 0.0826 0.0678 0.0533
0.891 0.903 0.906 0.908 0.909 0.915 0.922
rxI.
Mean 1.30 a . d . 0.015
The results are shown in Table 11. Columns 11,111,and IV give the concentrations of total HI, total HI,, and I, respectively. Column V gives the values of the constant, [ZHIl [Izl = k,. Column VI gives the measured PHI31 values of the specific conductances L of the solutions and column VI1 the values of r, the degree of ionization of the H I and the HI, in the solution, calculated on the assumption that both acids are ionized to the same degree. These values were computed by means of the relation
L . 103
(1 7) [EHIIAO,l -k [ E H 1 3 1 A o ~ ~ d ' For AoHI the value 440 was employed. For AoH13the value AoHIAI- + AIa- = 440 - 76 41 = 405 was employed, the value A,; = 41 being that determined by Bray and MacKay. Column VIII shows the values of the total-ion concentration [XC,]= r([EHI] + [EHI,]), and column IX shows the values of rHI for solutions of HI having the same total-ion concentration. The values of jHI were interpolated from a y-$-curve drawn from the data given in Table I. From the values of k, shown in columnV i t is evident that for ion concentrations between 0.15 and 0.05 N , k, is aconstant and equal to 1.30.10-~, with an average deviation for the seven experiments of only 0.015 or This agrees, within the experimental error, with the results ob1%. tained by Jakowkin2 who made a similar series of experiments with HI using CS, as the second phase. His values for k, vary between 1.30 and 1.35 with an average of I.32.10h3.
+
l
Bray, THIS JOURNAL, 33, 1193 (1910). 21 (1896).
* 2.QhysiR. Chem., 20,
THE
LAWS OF CONCENTRATED SOLUTIONS.
V.
693
Moreover, a comparison of the figures in columns VI1 and I X shows that the average deviation of y for the mixture from y for pure H I solutions a t the same total-ion concentration is only o.8yo which must be considered as within the experimental error, since the method of computing y for the mixture neglects the varying influence of the viscosities of the different mixtures. This agreement supports strongly the assumption that the two acids H I and HI, are ionized to the same degree in solutions of the same total-ion concentration. Bray and MacKay found the same to be true for the two salts KI and KI,. 8. The Ionization Constant of Arsenic Acid. Walden’ has measured the conductance of solutions of arsenic acid, and of mono-sodium and mono-potassium arsenates a t 25O. By plotting values of (Cy)” against those of I / A , using n = 0.45 for the sodium salt and n = 0.50 for the potassium salt, the value A. = 86.5 is found for the sodium salt and the value A. = 1 1 2 for the potassium salt, both values being expressed in reciprocal ohms. By subtracting from these two values the equivalent conductance of the sodium ion 51.2, and that of the potassium ion 74.8, respectively, the two values 35.2 and 37, respectively, are obtained for the equivalent conductance of the H,AsO,ion. The value AHzAsOa= 36, was adopted, and may be in error by one or two units, owing to hydrolysis of the salts, especially a t the lower concentrations, but i t is sufficiently accurate for the present purpose. Then if the equivalent conductance of the hydrogen ion is taken as 36 I , A, for arsenic acid is 397. The ionization constant of arsenic acid calculated from Walden’s conA2C is then 4.45 X ductance data by use of the formula k,,, = A0 (A, - A) IO-^ in the most dilute solution, 0.002 n, where Ci = 0.0015 and it increases with increasing ion concentration. I n order to determin the ionization constant a t the ion concentrations used in the equilibrium measurements, the conductances of several hydrochloric acid solutions were measured, and then to the same solutions known amounts of arsenic acid were added and the conductances redetermined. The concentrations of the various molecular constituents of the mixture were then calculated by means of the relations
and [H,AsO,]
=
[XAS] - [H,AsO,-],
Ibid., 2, 52 (1888). a Cf. Luther, 2. Electrochem.;13, 297 (1907).
(20)
EDWARD W. WASHBURN AND E A R L E K. STRACHAN.
694
I, being the specific conductance of the pure hydrochloric acid and L’ that of the mixture.
The results are shown in Table 111. The last column
of the table shows the values of k,,,
=
.[Hf [ H z A z l, which evidently
[H&O4 I decreases regularly with decreasing ion concentration. I n order to express TABLEIII.-CONDUCTANCEAND
I. [2”C1].
103.
126.8 101. I
50.57
11. L.
111.
0.04903 0.03952
o.05004 0.04071 0.02219
0.02022
I-’.
IONIZATION OF H,AsO, IN SOLUTIONS OF HC1.
IV. [HzAsO;]..
V.
VI.
10s. [H f ] . 103
. [H~AsO,].103.
114.8 93.6 51.4
2’. 52
2.99 4.99
50.4
VII.
k
~103.~
50.0
5,75 5.60
47.8
5.30
,
this “constant” as a function of the ion concentration Ci, the Kraus equation’ k,,, = k DC,“ was employed, giving
+
[“I
+
[H,AsO,-I - 4.32 4c:’z, [ H , A S O ~which holds for the range of total-ion concentrations involved in the final equilibrium measurements. 9. The Ionization Constants of Arsenious Acid. Arsenious acid is a very weak acid having an ionization constant2 of 2 . IO-*and hence in the presence of a strong acid its ionization as a n acid is quite negligible. Owing to its amphoteric nature i t can, however, function as a base in a strongly acid solution. This is shown by the decrease in the conductance of hydriodic or of hydrochloric acid which occurs when arsenious acid is added to the solution. Its ionization as a base may be expressed by the readtion H,AsO, = AsO+ OHH,O giving the ionization constant
+
+
where H,AsO, is understood to mean the sum of the concentrations of all the unionized forms in which the substance exists in the solution.S In order to determin the constant has, the following experiment was resorted to. The specific conductance L of a 0.1 N hydrochloric acid solution a t 2 5 O was found to be 0.03952. After dissolving 0.0494 formula See Bray, Trans. Amer. Electrochem. Sac.,
21,
144 (1912);Noyes and Falk,,
THISJOURNAL, 34, 484 (1912). Zawidski, Ber., 36, 1433 (1903). Thus the following forms may exist, H,AsO,, AsOOH, As(OH),, etc. The freezing-point measurements of Raoult ( A m .chim. phys., 2 , 84, I IO (1884)),and the boilingpoint measurements of Biltz (2. physik. Chem., 19,422 (1896))and of Zawidski (Ber., 36, 1429 (1903))show that no polymerization occurs.p
THE LAWS OF CONCENTWTED SOLUTIONS.
V.
695
weights of '1, As,O, in a liter of this solution the specific conductance was found to be L' = 0.03886. We have, therefore,
[OH-]
=
(AH+
+ AC~-)IO-~~ 1oS.L
1
and
From Zawidski's conductance measurements on solutions of NaH,AsO,, the conductance of the H,AsO; (or As0,-) ion is found to be 3 I. j. Reasoning from analogy we may, therefore, conclude that the conductance of the AsO+ ion will be about 40 reciprocal ohms. Equation (2j) gives, therefore, Iz,, = 0.13.10-~*which agrees well with the value 0.I 8 . 1 0 - ~ ~ which can be calculated from similar measurements carried out by Zawidski, who used hydriodic acid in place of hydrochloric. IO. The Measurement of the Arsenious Acid-Iodine Equilibrium. Experimental Procedure: Experiments r-6.--The equilibrium vessel consisted of a two-liter, glass-stoppered bottle of resistance-glass, which was filled in the following manner : The air was first displaced by a rapid current of nitrogen and then the desired amounts of solid iodine, carbon tetrachloride, and arsenious acid solution were introduced, the first by allowing i t to fall in a fine powder through the nitrogen, and the two liquids from their respective stock bottles by means of nitrogen pressure. The bottle was then stoppered and sealed with Khotinsky cement. If the equilibrium was to be approached from a higher temperature, the mixture was allowed to stand a t room temperature (about 30') for two days before being placed in the thermostat, but if from a lower temperature, i t stood in the ice chest for two days. When the bottle had been rotated in the thermostat for 24 hours at 25O, it was opened and the contents analyzed, preliminary experiments having shown that equilibrium was reached within twenty-four hours, which agrees with the observations of Roebuck. The water layer was removed by means of a pipet, afid transferred to a weight buret,' from which portions were weighed out for analysis. In order to obtain samples of the carbon tetrachloride layer, a pipet having its lower end sealed together and blown out into a thin bulb was employed. This was lowered into the carbon tetrachloride, and the bulb broken against the bottom of the bottle. The samples were transferred to weighed flasks and weighed. The densities both of the water layer and the c'arbon tetrachloride layer were measured in order that the concentration by volume might be calculated. The iodine in the carbon tetrachloride was Fig., THISJOURNAL, 30, 40 (1908).
696
EDWARD W. WASHBURN AND EARLE K . STRACHAN.
determined by titration with tenth normal thiosulfate. In some experiments the free iodine in the water layer was reduced to hydriodic acid by sodium sulfite. The solution was then diluted to about hundredth normal, made acid with nitric acid, and the hydriodic acid precipitated by very dilute silver nitrate. I n other experiments, the water layer was titrated with tenth normal arsenious acid, after the addition of sufficient disodium phosphate to make i t just neutral when the end point was reached.' By either method the total iodine in the aqueous layer can evidently be calculated. The concentrations of the various molecular species present were then computed by the methods outlined in section 3. The results are shown in Table 117. I n order to illustrate the calculation of these values from the experimental data, the calcuhtion for experiment number I is here given in detail. The analytical data are [XAs] = 0.10128 gram atom per liter, [XI] = 0.18568 gram atom per liter, and [Iz] in the carbon tetrachloride layer = 0.005325 mol per liter. Reference to figure on p. 689 shows that a t this concentration of iodine the partition constant is 85. I , hence [Ia]in the water layer = 0.005325 85. I
0.0000625. Preliminary calculation showed the total ion concentration to be 0.153, and from the r-yC-curve prepared from the data given in Table I, the degree of dissociation of H I and HI, in this solution is found to be 0.885. Substituting these values in equation (6) we obtain I
0.885 ~
[I-]
3 0.0000625 [I-] +-___ 0.885 1 . 3 0 x IO+
=
*
0:1857 - 2 X o.ooo06
(26)
which, when solved, gives [I-] = 0.1433. Then, on substituting this value in equations (7), (8), and (9) the following results are obtained: 1-0.885 x 0.1433 = 0.01866, [HI] = 0.885 0.0000625 X 0.1438 1.30 X IO-^
[I;]
= _ _ ~ _ _ _ _-
[HI31
I
=
- 0.885 0.885
x
0.00690
0.00690,
=
0.000903.
The total arsenic-arsenic concentration is obtained by use of equation (IO) as follows: [H,AsO,] [H,AsO,-] = 1/2(0.1438 0.0186 0.0069 0.0009) = 0.08510. (30) Assume as a first approximation that
+
+
+
+
+
[€I+] = [I-] [I,] =
(0.1433
+ 0.0069) = 0.1502.
Washburn, loc. cit., THISJOURNAL, 30, 31 (1908).
(31) (32)
THE LAWS OF CONCENTRATED SOLUTIONS. V .
Now, JzAs,, the dissociation constant of arsenic acid, = (4.32 x IO-^. Hence, 0.08510 [H,AsO,-] = 5 87 X IO-^ X ___ = 0.00333. 0.1502
697
+ 4(0.153)'.') (33)
For a second approximation, [H'] = [I-] [Is-] [H2AsO4-] (34) = 0.1433 -k 0.0069 $. 0.0033 = 0.1535 (34) and 5.87 x IO-3 x 0.08177 ___[H,AsO;] = = 0.00313. (35) 0.1535 A third approximation gives practically the same value, 0.003 14, for the concentration of the arsenate ion. Hence, [H,AsO,] = 0.08197 and [ H f ] = 0.1533. By substituting the above values of the arsenic acid and the arsenate ion concentrations in equation (3), we find that [HsAsOs] + [AsO+] = 0.10128 - 0.08510 = 0.01618. (36) Then from equation ( 1 2 ) we obtain [AsO+] = 0.13 X 0.01618 X 0.1533 = 0.00032. (37) Hence, [H,AsO,] = 0.01586, (38) and
+
+
Experimental Procedure: Experiment 7.-Experiment 7 was undertaken for the purpose of ascertaining the effect upon the equilibrium constant, of a large variation in the value of [ H + ] in the solution. The only practicable method by which this variation can be effected is by the addition of a n iodide to the equilibrium mixture. Experiment 7 was, therefore, carried out as follows: 116 grams of potassium iodide and 30 cc. of a o.og553 normal iodine solution containing 0.12 formula weights of KI per liter were mixed with 50.97 grams of a 3.530 formal solution of H,AsO, and 30.52 grams of a 0.05870 formal solution of H,AsO, and the whole made up to a volume of 6 liters. This mixture was then shaken in a IOliter bottle with 1350 cc. of carbon tetrachloride for 24 hours a t 25O. The carbon tetrachloride layer was found on analysis to contain 1.49. IO-^ formula weights of I, per liter. From this figure and the original composition of the mixture the values shown in the table are readily calculated. The concentration of potassium ion in this solution when equilibrium was attained was 0.1021 equivalents per liter. The Conductance of the Equilibrium Mixture.-B y measuring the specific conductances of the equilibrium mixtures a check can be secured upon the
EDWARD W. WASHBURN AND EARLE K. STRACHAN.
698
experimental results and the calculations. Such measurements were made in all but the first two experiments. Column 15 in Table IV shows TABLEIV.-ARSENIOUS ACID CONCENTRATIONS, [ 1, [H,AsO,]
IN
IODINE EQUILIBRIUM AT 2 5 O. DATAAND RESULTS. FORMULA WEIGHTS PER LITER-AT-25'.
. [ H f I a .[I-Ia -- K,.
1912 Atomic Weights. 4.
2.
3.
.
[TI]. 108.
[rasl . 108.
I*
I ,0232
101.28
2
I ,0250
3* 4* 5* 6
,0140 I .OI 55 I .or48 I .Or44
185.68 206.86 90.59 107.34 102.48 101.40 ....
1.
EXP No.
Densit:
25'/25
I
I
7. (1-I. 103. I* 2
3*
4* 5" 6 7
I* 2
3" 4* 5* 6 7
143.3 146. I 80.79 83.12 83.97 84.02 I O 1 .OO
8.
101.21
51.98 49.37 49.35 49.34 .... 9.
[Is-]. 108.
[H+]. 108.
6.904 84 0.442 4.599 2.878 2.548 0.136
153.3 160.1 83.97 90.51 89.62 89.36 9.63l
IO.
5.
. 108.
c i . 103.
0.0625 0.0943
I54 I 60 84 90 90 89 111.7
[I21
0.00727
o ,0720 0.0446 0.0394 0.0175 10. [AsO+] ,108.
11. [HaAsOs] .loa.
0.32 0.25 0.080
O.oo00
17.
[HASO,] ,103.
Lcalc.
Lcalc.-Lobs.
..... .....
.....
0 * 03657
0.00025
0.03926 0.03900 0.03882 0.01g18
0.00030 0.00036 0.00014
0.00021
Mean
Mean a. d. Max. d. P. E.
0.906 0.904 0.904 0.904 0.862 12.
[HzAsOi-1.108.
3.14 3.18 2.74 2.79 2.78 2.79 10.60
7.07 0.832 1.301 1.437 0.253
16.
Y I&
0.882
15.86
0.010 0.015 0.017
-r
0.884
I 2 .OO
13.
81.97 85.78 44.83 45.73 45 :25 45 109 19.60
6.
in1
392 0.400 0.290 0.300 0.300 0.298 0.333
0
0.330 h0.038
the measured values of the specific conductances L of the various equilibrium mixtures, and column 16 the values I,' calculated from the corresponding ion concentrations shown in columns 7, 8, 9 and 12, by means of the usual equation
IO*.L' = [H+]A,+
+ [I-]AI- +
[13-]AIa-
+
+ [K+IA K + * Indicates equilibrium approached from higher temperature. [H,AsO;
[K+] in this experiment was 0.1021.
IAH&O*-
(40)
THE LAWS OF CONCENTRATED SOLUTIONS.
V.
699
employing the values A,+ = 361, AI- = 76.5, Ala- = 41, AH2AS0,-36 and A,+ = 74.3. I t will be noticed that the calculated and observed specific conductances differ on the average by only 0.6%~ which is better agreement than could justly be expected, since the relative viscosities,of some of the mixtures were as large as 1.03 and the effect of this factor is only partially allowed for in the above method of obtaining the calculated values. 11. The Equilibrium Constant and the Mass Action Law. The values of
.are given in column 14 of Table IV. I t will be noted that the mean value of this constant is 5.5.10-~,with an average deviation from the mean for the seven experiments, of only 3.5% and a m a x i m u m deviation of only 6 % , the “probable error” being 1.270. Moreover, these small deviations are evidently irregular and without significance. We must, therefore, conclude that under the conditions of the above experiments, this equilibrium obeys the law of mass action within the small experimental error of 4%. To appreciate the f u l l signi$cance of this result, the ranges of variation undergone by the concentrations of the diflerent substances in the series of experiments should be carefully noted. T h e y are as follows: [ I a ] ,f r o m 0.000007 to O.OOOOQ molal or 13-fold; [I-],from 0.08 to 0.14 normal or nearly a-fold; [I3-],from 0.00014 to 0.011 or 8o-fold; [H+], from 0 . 0 0 ~to 0.16 or more than 16 fold; [H,AsO,], from 0.00025 to 0.016 or more than 60-fold; [H,AsO,], f r o m 0.02 to 0.086 or more than 4-fold. The smallest concentration range covered by any of these substances is that for the iodide ion, about 2-fold, but since the concentration of this substance appears as the cube in the expression for the equilibrium constant, the effect of this vanation is increased 3-fold and thus becomes comparable with the others. The case of the hydrogen ion is especially interesting for since its concentration appears as the square in the expression for the equilibriumconstant, its large variation of 16-fold might be expected to show up any abnormality in its behavior by a corresponding effect upon the equilibrium constant. If the concentrations of the molecular species concerned in the equilibrium were expressed in terms of mol-fractions, z, instead of mols per liter, the corresponding constant K z would be related to the constant K , in the following manner, K, = K, * “20 * (2n)a where nH20 is the number of mols of H,O and ( 2 n ) the total number of mols of all the molecular species contained in one liter of the solution. If k, is a true constant, ) ~ . then the same will be true of K, except for variations in the factor n ~ ~ ( 2 n For t h e range of concentrations included in the present investigation this factor does not vary by more than two per cent. of itself and hence the constant K, is a sufficiently satisfactory basis for expressing the results.
700
EDWARD W . WASHBURN AND EARLE K . STRACHAN.
No such effect is noticeable, however, and, if present, must be almost exactly compensated by some other influence. PART 11. A GENERAL LAW FOR CHEMICAL EQUILIBRIUM IN SOLUTIONS CONTAINING IONS. BY EDWARD W. WASHBURN.
The Theoretical Interpretation of the Behavior of the Arsenious AcidIodine Equilibrium with Respect to the Mass Action‘ Law. The comparatively simple reaction AB = A+ B- typifying the ionization of a strong electrolyte of the uni-univalent type involves only one un-ionized molecule and two ions and yet we know that this simple equilibrium does not obey the law of mass action, even approximately. The results described in the preceding section demonstrate, beyond question, however, that the much more complex equilibrium H,AsO, 1,H,O = H,AsO, 2Hf 31involving 3 species of un-ionized molecules and 3 species of ions obeys the law of mass action within the experimental error of the measurements, for a fairly large range of concentrations. Certainly if there is any reat deviation from the requirements of this law i t can only be one which would cause the equilibrium constant to change by less than 5% of itself, a change which is quite insignificant compared with the large variation observed in the ionization constant of a strong electrolyte. The contrast between these two equilibria is a very striking one for which no adequate explanation is offered by our present theory of solution. Indeed the behavior of the simple ionization equilibrium is usually spoken of as the “Anomaly of the Strong Electrolytes.” Owing to the exact thermodynamic relations which bind together all of the laws of solutions, i t is evident that the question of a satisfactory theoretical explanation for the above behavior is part of the whole problem of the quantitative formulation of a theory for solutions of strong electrolytes. The purpose of this portion of the present investigation is to propose an equation of state for solutions containing ions which can be made to serve as the basis for erecting a system of laws which will express quantitatively all of the known facts concerning these solutions. 13. An Equation of State for Solutions Containing Ions. Let us consider a solution made up of the molecular species A, B, C, etc., in the proportions expressed by the mol fractions x,, x B , xc, etc. If we change the mol faction of any one of these species, say A for example, by the amount dx, then the corresponding change in its partial vapor pressure p, above the solution will be expressed by the equation‘ I 2.
+
+
+
dP.4
+
=f*(MW*
+
(41)
Strictly speaking, only if the vapor is a perfect gas. See, however, the last three paragraphs of this section.
T H E LAWS OF CONCENTRATED SOLUTIONS.
V.
701
wheref,(M) is a function of the nature of the medium or the“thermodynamic environment”‘ prevailing within the solution. I? ideal solutions and in sufficiently dilute solutions, fA(M) is a constant with respect to variations in xA and hence for this class of solutions we can write dp, = kAdXA (42) which on integration gives P A = kAX.4’ (43) the integration constant being zero. This equation will be recognized as Henry’s law with the concentration expressed in terms of the mol fraction instead of in mols per liter. If the solution is an ideal solution or if A is the solved and the solution is dilute, then k , is evidently equal to poA, the vapor pressure of pure liquid A a t the same temperature, and we have P A = POAXA, (44) which is Raoult’s vapor-pressure law. By purely thermodynamic reasoning we can derive all of the laws of ideal solutions and of “sufficiently dilute solutions” from equation (42) and the important fact to be noted here is that in deriving these laws the assumption is always made (usually implicitly) that f,(M)is a constant. I n other words, the laws of dilute and of ideal solutions have no theoretical basis except for solutions in which the thermodynamic environment i s a constant. For a solution in which the thermodynamic environment M is not a constant, the form of the function f ( M ) must be known before a set of laws for such a solution can be derived, and since no two “concentrated” solutions are exactly alike, the form of this function and the terms in which it is best expressed would, in general, be different for every different solution. An attempt to treat every different solution as a problem by itself would, however, make the construction of a satisfactory theory or theories of “concentrated” solutions too tedious a process to be undertaken. When confronted with a situation of this kind further progress is frequently best accomplished by a process of classification, that is, certain solutions may be treated as a class owing to the possession of some common characteristic which is chiefly responsible in determining the thermodynamic environment which prevails within them. Now solutions of strong electrolytes a t concentrations above 0.001 normal belong preeminently to the group of solutions for which the thermodynamic environment is not a constant, but is instead a variable which changes very rapidly with the concentration of the electrolyte. Moreover, the systematic and comprehensive investigations carried on during the past ten years by A. A. Noyes and his associates have made Cf. Trans. Amer. Electrochem. SOC.,22, 331 and 333 ( 1 9 1 3 ) .
702
EDWARD W. WASHBURN .4ND EARLE K . STRACHAN.
it very clear that the thermodynamic environment in dilute solutions of electrolytes is almost entirely determined by the i o n concentration in the solution, and that, therefore, f ( M ) in equation (41) may be most advantageously expressed in terms of this variable. Equation (43) would become, therefore, P A = fA(‘dXA (45) and it remains only to determin the best form for the function f(C,), Now i t must evidently be of such a form that it will reduce to kA when Cibecomes zero. In lieu of any theory or hypothesis which would assign any special form to this function the usual procedure would be to write f A ( C i ) = k,(I PACi L”,C2 ) (46) and it is evident that with the aid of thermodynamics we could build up a complete set of laws on the basis of this relation and that this set of laws could be made to hold with any desired degree of exactness, if a sufficient number of terms were included in the above series. A. A. Noyes and his associates have found, however, that the number of empirical constants required to express the results of experiment is in many instances reduced if C j is taken as the variable instead of C, h. being almost a universal constant which varies only between the comparatively narrow limits, 0.4 and 0.6, in aqueous solutions. If, therefore, we adopt this quantity as our variable and agree to restrict our considerations to such ion concentrations that the terms of the series containing the higher powers of C,” are negligible in comparison with that containing the first power of the variable, then we can writel
+
+
+....
f A ( C i ) = k A ( I f k’Acf)* Combining this equation with equation (45) above we have
(47)
+
P A = kA(1 kkC:)XA (49) as our equation of state for solutions containing ions. The constant Ll expresses the influence of the thermodynamic environment (in so far as this factor is in turn determined by Ci) upon the vapor pressure of the molecular species A above the solution. For two molecular species in the same solution the relation between their constants L’ is determined
The series converges very rapidly for values Ci not greater than say 0.25 and a t present i t would not be advisable in most cases to attempt to include more terms in it, owing to the uncertainties which arise in connection with the determination of the correct value of Ci a t much higher concentrations. The above function contains two empirical constants, k’ and h, for expressing the effect of Ci upon the thermodynamic environment. I t might perhaps be fully as satisfactory to take h = l/z in all cases and to write the function in the form (I -k k’ACii2)
fA(Ct) =
(I
+ k”AC$’”)’
for example, where k”A is a second empirical constant which is much smalbr than
THE LAWS OF CONCENTRATED SOLUTIONS.
V.
703
solely by the nature of the two species. The constant h is probably determined chiefly by the .nature of the ions which determin the thermodynamic environment and, as mentioned above, is very nearly the same for all ions and may be taken as approximately equal to f a . Starting with the above equation of state it is evident that the derivation of a complete set of laws for solutions containing ions involves nothing but pure thermodynamics and offers no particular difficulties. Since, however, in the present paper we are chiefly interested in the law governing chemical equilibrium in such solutions, we will confine ourselves to the development of this law and will reserve the development and testing of the other laws for some of the succeeding papers ‘of this series. Before proceeding to the derivation of the law for chemical equilibrium i t should be noted that our fundamental equation of state has been formulated in terms of vapor pressure. It might, of course, equally well have been expressed in terms of osmotic pressure i ~ of , fugacity 9,of activity 5, or in terms of Gibbs’ molecular thermodynamic potential p, or of any of the other thermodynamic functions which have been employed by different writers. In fact, any one of these other systems would have given us a more rigorous formulation of our equation of state, for equation (49) implicitly assumes that the vapor of A is a perfect gas. Strictly speaking, therefore, the quantity PA in equation (49) must be understood to signify the actually measured vapor pressure corrected for the effect of any deviation from the perfect gas law. The vapor pressure so corrected, 9,has been called by Lewis the “escaping tendency” or the “fugacity.”’ and i t is, therefore, strictly speaking, this quantity which should be understood when the term vapor pressure is employed in what follows. Practically, however, the two are identical for all the cases which we shall consider. In terms of osmotic pressure n, the equation of state would read as follows: dn,
or
=
-RT
_VA
d log,
X,
(I
+ KaC;)
(50)
+
nAVA = -RT log, xAK,(1 KbCf) (51) where kA is an integration constant whose value depends upon the nature of the liquid phase into which the constituent A is considered to be removed osmotically. This liquid phase may be the pure solvent, i t may be pure liquid, A, or it may be an entirely hypothetical incompressible liquid which serves as the intermediary during the osmotic removal of the constituent A from one solution preparatory to its being transferred to
’
Lewis, Proc. Amer. Acad., 37,54 (1901). The quantity # has also been employed very recently by Gay (/. chim. phyys., IO, 197 (1912)) under the name “expansibility tension.”
704
EDWARD W. WASHBURN AND EARLE K. STRACHAN.
another; for the only purpose which the concept of osmotic pressure plays in solution theory is that of a device by m e a s of which the maximum work involved in changing the mol fraction of any constituent of a solution may be conveniently visualized. In terms of the molecular thermodynamic potential ,u (in a sense similar to that in which this quantity was employed by Gibbs), the equation of state reads P A - RT log, x , ~ , ( I kiC$), (52) where k , is again an integration constant which is a function of the temperature and which depends upon the standard state chosen for reference. In a perfectly analogous manner the formulation, in terms of activity 4, gives us [A = k A ( I f k a c a ) x r (53) 14.A General Law for Chemical Equilibrium in Solutions Containing Ions. Let the chemical reaction be expressed by the equation aA bB = mM nN (54) The vapor pressures of the substances concerned in the equilibrium will be PA, PB . . . p M , p N etc., and in the vapor above the solution the equilibrium will obey the law
+
+
+. ..
+
+. ..
...
Now, according to our working hypothesis, if the solution contains ions, the vapor pressure of each of the substances A, B , etc. , will be expressed by the relation
p
= L(1
+ k'C2)X.
If we combine this relation for each substance with equation ( 5 5 ) above,' we have x b . x;. . K, h i kk-- . ( I L ~ C ~ ) " (+I k b C l ) b . . . (5 7 ) LZ k; . . x i xi . (I kMCq)"(T+ k ' , c p . . as the general expression for chemical equilibrium in a solution containing ions. We will now assume that the mol fractions x,, xB, etc., are so small in comparison with the mol fraction of the solvent that the mol fraction of each substance will be practically proportional to its volume concentration, i. e., that xA = const. X [A], xB = const. X [B], etc. Under these circumstances our general equation ( 5 7 ) may be written (I kaC-;)"(I L'BC h ) b . z.. [MI" [N]".. _ ~ _ _ _ -L ' (58) (I k&f)"(I + k X C a ) R . . . [A]" . [B]b . . .
.
.
.
.
.
.
.
.
+ +
+ +
.
+
Or employing osmotic pressures, if we combine equation ( 5 0 ) above with the = o (Washburn, THISJOURNAL, 32, purely thermodynamic relation (PmV,dn,) 484, Equation 30a ( I ~ I O ) ) ,we have the same equation ( 5 7 ) .
THE LAWS OF CONCENTRATED SOLUTlONS.
V.
705
an expression which evidently reduces to the mass action law if C, is either constant or sufficiently small, that is, whenever the thermodynamic environment becomes constant. We will now apply this equation first to the reaction of ionization of a strong electrolyte and then to the arsenious acid-iodine equilibrium. 15. Application of the General Law to the Ionization of a Uni-Univalent Electrolyte. For the reaction AB = A+ B-, the general equation (58) becomes k(1 k;,c;) [A+l[B-l (59) (I kpp)(I k&)* [AB 1 Performing the operations of multiplication and division as indicated and rejecting the terms containing the higher powers of Ct, this may be written
+
+
+
+
This is the Kraus equation for the ionization of a uni-univalent electrolyte and has been found by Kraus and Bray’ ta have an extraordinarily wide range of application, holding very exactly for both strong and weak electrolytes and for a great variety of different solvents. Our equation of state leads, therefore, to an expression for the ionization equilibrium of a uni-univalent electrolyte which corresponds exactly with the known behavior of such an electrolyte. I t tells us that obedience to the mass law is not to be expected unless Ci is kept constant or unless it is negligibly small, which latter condition is only fulfilled in extremely dilute solutions in the case of strong electrolytes.
16. Application of the General Law to the Arsenious Acid-Iodine Equilibrium. For this equilibrium our general relation (58) assumes the form
Now the constant k‘ for any molecular species in a given solution is a characteristic property of that species and the more closely two species of molecules resemble each other, the more nearly will their values of this characteristic constant approach each other. Hence we may expect the constants ka, and ka,, to be not far from the same order of magnitude and therefore the ratio
to be practically equal to unity for the range of ion concentrations covered by the experiments. This amounts to the statement that if two molecular Bray, Trans. Amer. Electrochem. SOC.,2 1 , 143 (1912).
706
EDWARD W. WASHBURN AND EARLE K . STRACHAN.
species which resemble each other very closely are in solution together, any change in the thermodynamic environment in the solution produces the same percentage change in the vapor pressures or the activities of both species, so that the ratio of the vapor pressures or activities remains constant. If for the remaining expressions of the right-hand member of equation (61) we perform the multiplications and divisions indicated and put h = ‘ I 2in the result, we have I (kka- - 2kk+ - 3k;-)Ci/2, which may be written with sufficient approximation for our present purposes I - 4k’Cyz, where k’ is an average value of this characteristic constant for the uniunivalent ions. In order to know what variation is to be expected in the quantity I - 4k‘Ci/2, for the range of ion concentrations covered by the experiments shown in Table IV, it is necessary to determin the order of magnitude of the constant k’. I n order to do this we shall employ the solubility-product law which follows from our equation of state (49). This law can be written in the following form :
+
or if as an approximation we put h = and ka+ comes, (A+)(B-) = K(I - 2k’Ci/2).
=
kk-
=
k’, this be(64)
Using the solubility data for TlCl a t 25O as given by Bray’ we find k = 0.I 75 and K’ = -I (approx.). The expression I - 4k’Ci/z can, therefore, bk written I 4Ci/z with sufficient exactness for our present purpose. Column 18 of Table IV shows the values of Ci/z for the different experiments shown in this table. From the figures in this column it is evident that we can write Cy2 = 0.330 3 0.038, and the expression I 4CtIz becomes, therefore, 2.32 & 0.14 or 2.32 (I f 0.06). The general expression for the arsenious acid-iodine equilibrium, equation (61), reduces, therefore, to
+
+
[H,AsO,] [H+I2[I-l3
= 2.3kC(1 f 0.06). (65) [H,AsQ 1[I; 1 I n other words, the same equation of state which leads to the Kraus equation for the ionization of a uni-univalent electrolyte also tells US that we may expect the arsenious acid-iodine equilibrium to obey the massaction law within a t least 6% for the range of ion concentrations included in the experiments recorded in Table IV, a conclusion which corresponds THISJOURNAL, 33, 1674 (1911).
THE LAWS OF CONCENTRATED SOLUTIONS. V.
707
perfectly with the behavior of this equilibrium as illustrated by the data given in that table. In both instances the same general law governs the equilibrium. The fact that in the case of the arsenious acid-iodine equilibrium this general law reduces to the mass-action law is due largely to the circumstance that in this equilibrium an un-ionized molecule appears on both sides of the equation, coupled with the additional fact that in the experiments recorded in Table IV the ion-concentration covered a comparatively small range. The true mass law constant of this equilibrium, that is, the value approached by the equilibrium function as the concentrations of all the reacting substances approach zero, is not the constant Ki shown in Table IV but is instead the constant k, of equations (61) and (65). From the latter equation we may calculate the value of this constant as follows: 2.3kC = K , = 5.5.10-~, and hence k ,
=
2.4.10-~.
(66)
This calculation, of course, rests upon the value, minus unity, which was assumed above as an average value of the characteristic constant k' for the uni-univalent ions, a n assumption which for the present must be regarded as only approximate. Concluding Discussion.-According to the fundamental hypo thesis expressed mathematically by our equation of state it is evident that there is no such thing as an "anomaly of the strong electrolytes" in the sense in which this expression is usually understood. The ionization of these electrolytes behaves toward the mass-action law just as any other chemical reaction does under similar conditions, that is, these electrolytes can not in general be expected to obey tho mass-action law unless the thermodynamic environment (which in this instance means practically the ion concentration) is kept constant. Even for a n equilibrium which involves no ions whatever, the mass law expression [Ml"[Nl". . * will not, in [AI4[Blb. general, be a constant, if whenever we shift the equilibrium by changing the concentrations of the reacting molecules, we, a t the same time, alter the environment which surrounds them, either by changing, for example, the temperature, or the ion concentration or by adding any other foreign molecules to the solution. The only anomalous behavior, if we can call it such, which strong electrolytes exhibit, is that the ions resultingfrom their dissociation produce upon the thermodynamic environment a much greater effect in proportion to their numbers than is produced by most uncharged molecules. The effect is produced, however, when any foreign molecule is added to water and it varies in magnitude and in specific nature with the nature of the added molecule, but for solutions not stronger than about a 0.1normal the mol fraction of the water is in most cases still large enough to practically control the thermodynamic environment. If the foreign
..
708
EDWARD
w.
WASHBURN AND
EARLE K . STRACHAN.
molecules are ions, however, the thermodynamic environment even a t such a low ion concentration as 0.001N appears to be appreciably different from that which prevails in pure water. This effect of ions upon the thermodynamic environment, is of course, much the same idea as that which has previously found expression in the terms “salting out effect,” “change in the ionizing power of the medium,” the “electrophilic” character of electrolytes,l and the “autolytic” conductivity of electrolytes.2 I n the treatment given in the foregoing pages the writer has simply pushed this idea to its logical conclusion and has attempted to give it quantitative formulation in the form of an equation of state for solutions containing ions, which, in so far as it is valid, gives us a t once a complete set of quantitative laws for such solutions, only one of which laws, that governing chemical equilibrium, has been derived and discussed in the present paper. In closing this discussion mention should be made of the recent contribution to this subject by G. N. Lewis3 where a point of view directly opposed to the one given above is set forth. Instead of assuming that the ions of electrolytes, even in dilute solutions, exert a marked effect upon the thermodynamic environment, Professor Lewis seems to prefer the views advanced by Jahn, according to which the thermodynamic environment in such solutions is assumed to be practically the same as that which prevails in dilute solutions of non-electrolytes and the apparently abnormal behavior of strong electrolytes is to be explained by the assumption that the conductivity method does not give the true degree of ionization. The evidence brought forward by Professor Lewis in support of his view is too important to be dismissed in a few words and, therefore, no attempt will be made to discuss it within the limits of the present paper. It is the writers’ intention, however, to consider this evidence in detail in connection with one of the succeeding papers of this series which will deal with the results of some investigations4 now being carried on in this laboratory upon the relation between viscosity, true transference numbers and ion conductances. PART 111. THE ENERGETICS O F THE REACTION.
17. The Heat of the Reaction. The heat of the reaction between arsenious acid and iodine in dilute aqueous solution may be calculated from the following thermochemical equations : Lewis and Wheeler, Proc. Amer. Acad., 41, 429 (1906). Bousfield and Lowry, Phil. Trans., ( A ) ,204, 2 5 6 (1905). Lewis, “The Activity of the Ions and the Degree of Dissociation of Strong Electrolytes.” THISJOURNAL, 35, 1631 (1913). The nature of these investigations was outlined in the preceding paper of this series. Sce also Washburn and Williams, THIS JOURNAL, 35, 750 (1913).
THE LAWS OF CONCENTRATED SOLUTIONS.
H,AsO,(Aq) + O(Aq) H2O (liq) 0 (gas) H,(gas) I,(solid) (Aq)
V.
709
H,AsO,(Aq) + 39,205 (1) H,(gas) O(gas) - 68,303 (2) = O(Aq) 1,487 (3) = 2H+ 2126,400 (4) 13= I,(&) 1- 3,820 (5) 1,(Aq) = I,(solid) 6,390 (6) H,As03(Aq) + H,O + I,- = H,AsO,(Aq) 2H+ 31- 1360 cal. I n the case of the first, second and fourth of the above reactions the values given are taken from Thomsen (“Thermochemische Untersuchungen”). The heat of solution of oxygen (reaction 3) and that of iodine (reaction 6) were calculated from the solpbilities of the substances a t two different temperatures by means of the equation S AH = R log _2 c e SI I n the case of oxygen Winklerl and Bohn and Boch’ have determined the solubility a t various temperatures and from their data the values S,,, = 0.004440 and Sso0= 0.003744 were computed for the solubility of oxygen under a pressure of one atmosphere. These values give AH = -2974 as the heat of solution (heat absorbed) per mol. In the case of iodine, Sammet, found the values Szse= 0.001342 and S, = 0.004160 mol per liter. These values give AH = 6390 as the mean molecular heat of solution of iodine between these two temperatures. I n order to obtain the heat effect of reaction 5 above, the values of the [I-I[I 1 = k , obtained by different logarithm of the equilibrium constant 2
+
+
= =
+
+
+
+
+
+ + +
+
k).
I
investigatorsS were plotted against the corresponding temperatures and the values k,, = 0.735. IO-^ and k,,, = 1.34. IO-^ obtained by interpolation. I n preparing this plot the values of k , employed at each temperature were those for an ion concentration of about 0.1 equivalent per liter. By means of the van’t Hoff equation the value A H = 3820 cal. was then calculated. The value AH = -1360 cal. for the reaction between arsenious acid and iodine, obtained from this set of thermochemical equations, corresponds to a multiplication of the equilibrium constant by the factor 1.1 for a rise of I O O . This is in good agreement with the observations of Roebuck4 who found values of this factor varying between 1.1 and 1.3 for the “constant” computed by him (cf. Sec. 2). Landolt-Bornstein-Meyerhoffer,Tubellen, p. 599 (3rd Ed.). cit. Fedotieff, 2. anorg. Chem., 69, 32 (1910); Jakowkin, 2. physih. Chem., Ij, 541 (1894); 20, 19 (1896); Dawson, J . Chem. SOC.,79, 238 (1901); 2. physzk. Chem., 56, 605 (1906); Bray and Mackay, Zoc. cit. LOC.cit., see note I , p. 685, above. l
a LOC.
7
0
EDWARD W. WASHBURN AND EARLE IC. STRACHAN.
By means of the van’t Hoff equation we obtain the general expression log,, K, = -I. 3495 0.00372 t (68) from which the equilibrium constant of the arsenious acid-iodine equilibrium may be computed for any temperature, t (Centigrade). 18. The Free Energy of the Reaction. Definition of the Term ‘(Free Energy.”-As a measure of chemical affinity the thermodynamic potential a t constant pressure (Gibbs’ C-function) is a more convenient function to employ than is the maximum work of the reaction, which under the name of “free energy” was first employed for this purpose by Helmholtz. For this reason and also because of the confusion which has arisen in connection with the use of these two functions, G. N. Lewis has recently’ proposed to transfer the name free energy to the former function and to employ this function (represented by the letter F ) exclusively as a measure of chemical affinity. The increase in free energy which accompanies any process would then be represented by the symbol AF and the partial free energy of any molecular species in a mixture by the symbol F. The latter quantity corresponds to the molecular thermodynamic potential and is the quantity represented by ,u in our equation (52) above. The value of AFO for any chemical reaction taking place in a medium of constant thermodynamic environment is given by the expression AFO = RTlog,K (69) where K is the equilibrium constant for the particular thermodynamic environment in question and the reaction is considered as taking place between the reacting substances a t such initial concentrations that their activities in this particular thermodynamic environment are each equal to unity and ending with the products of the reaction a t such final concentrations that their activities are also each equal to unity. It is clear, therefore, that the free energy of a chemical reaction depends upon the medium in which the reaction occurs. Thus in the case of the arsenious acid-iodine equilibrium we might calculate the value of A F o for this reaction in an infinitly dilute aqueous solution or we might calculate its value in an aqueous solution having a constant ion concentration of, say, 0.1equivalent per liter. In the former case we should employ the value K , = 2.4. IO-^ as the equilibrium constant (as explained above, see p. 707) while in the latter case the valueK, = 5.54. IO-^ would be employed. We shall consider here only the latter case. A F ofor the Arsenious Acid-Iodine Equilibrium-Putting K, = 5.54. IO-^ in equation (69) above we have AFrhSO = R T log, K = -7170 joules (70) or
+
Lewis, THISJOURNAL, 35, 14 (1913).
THE LAWS OF CONCENTRATED SOLUTIONS. V.
+
+
71 f
+
+
H,AsO, H,O I,- = H,AsO, 2H+ 31-; AFZOSO= -7170 joules in any aqueous solution having an ion boncentration not far from 0.1 equivalent per liter. The general expression for AFO for this reaction under the conditions stated, as obtained from equations (68) and (70), is -AFo = RT log, k, = 5690 5.42T (joules) (71) which holds for the range of temperatures within which the heat of the reaction may be assumed to be constant and equal to 1360 cal. 19. The Potential of the “Normal” Arsenic Electrode. Consider the wholly hypothetical cell H,AsO, 1,- P t H,AsO, ---f IPt -
+
I 1
1
H+ ‘ - ! I A B i
1 I
A B j prepared as follows: Solutions of the salt AB are prepared of such ion concentrations that when the cell is completed the thermodynamic environment (which can be controlled by means of AB) on both sides of the cell shall be substantially that which prevails in the equilibrium mixtures described by Table IV, that is, an ion concentration, of about 0.1 equivalent per liter must exist on both sides of the cell. In the left half the molecular species H,AsO,, H,AsO, and H+ are present a t such concentrations that the activity of each is equal to unity and in the right half the molecular species I,- and I- are present, also a t such concentrations that the activity of each is equal to unity. The potential E of this cell will be E = _ ~AFO ___ 7170 = 0.037 Volt. (72) 2 . 96,500 2 96,500 If we call the separate electrode potentials, the potential of the “normal” arsenic electrode (El,) and the potential of the “normal” iodine electrode (E;), respectively, we have Els E,” = 0.037. (73) The potential of the normal iodine electrode’as customarily defined is - 0 . 2 5 6 volt when measured against the normal calomel electrode. If this is also the potential of the “normal” iodine electrode as defined above -and it will not be far from it-we have E l s = 0.037 + 0.256 = 0.293 volt (74) as the potential of the “normal” arsenic e1ectrode.l ~
.
+
This statement is,made subject to the condition mentioned because our usual
E. M. F. equations are all derived on the assumption of a constant thermodynamic environment. They need to be revised on the basis of an equation of state which takes into account the change of thermodynamic environment with changing ion concentration. This revision will be undertaken in one of the future papers of this series. As an example of an E. M. F. equation based upon our equation of state (eq. 49) the
712
EDWARD W. WASHBURN AND GARLS K . STRACHAN.
Loimarantal attempted to measure directly the potential of the arsenic electrode by using a platinum electrode dipping into a mixture of arsenious, arsenic, and sulfuric acids to which a trace of potassium iodide had been added to act as a carrier and to make the electrode reversible. In a discussion of these measurements, Luther2 pointed out that no proof was given that the electrode was truly reversible under these conditions and the action of the oxygen of the air upon the iodide in the presence of the acid would have been a source of considerable error. From three of Loimaranta’s experiments Luther calculated the following values for the potential of the “normal” arsenic electrode, 0.322, 0.339, and 0.333. The mean of these, 0.33 volts, is 4 centivolts higher than the value calculated above from our equilibrium constant. Summary and Conclusions. Concentrations in. formula weights per liter. I . At infinit dilution and 25O the distribution constant for the partition [I2ICClr of I, between H,O and CC1, is _ _ - 85.0. [I2 1H20 2. The following equivalent conductances were determined for H I solutions at 2 5 O , at the equivalent concentrations indicated: 0.15 N , 389.5; 0.1N , 395.6; 0.08 N , 398.5; 0.05 N , 404.3. They are all more than 2 yo than Ostwald’s values. - higher 3. The value of the constant [I I [I-] a t 2 5 O in solutions of HI is (1.30 [ILI-I & .O.OI~).IO-~ for total-ion concentrations lying between 0.05 and 0.15 equivalents per liter. In a mixture of H I and HI, both acids are ionized to the same degree. 4. The value of A. for the H,As04- ion at 2 5 O is 36 reciprocal ohms. The ionization of H,As04 at 2.5’ can be expressed by the relation EH+ 1[H,AsO*-I _ _--10-~.(4.32 4C:l2), where Ci is the total-ion con[H,AsO*l centration in the solution. 5 . The basic ionization constant of arsenious acid a t 25’ is [AsO+][OH-] = 0.15 IO-’* in a solution having a n ion concentration of [H,ASO,~ 0.I equivalent per liter. expression for the E. M. F. of a silver nitrate concentration cell may be cited. The 20.
-’--
+
.
revised equation is
E
=
2RT log,
[I
+ k’(C’xl+- C ~ ~ + ) ] ”CAg+ __ 2
(75)
C’Ag+
which reduces to the Nernst equation when the ion concentration (in this case Ci = C A ~ + ) becomes sufficiently small. Loimaranta, 2. Electrochem., xj, 33 (1907). Luther, Ibid., 13, 291 (1907).
THE LAWS O f CONCENTRATED SOLUTIONS.
V.
713
6. The value of the equilibrium expression [H,AsO,] [H+l2 [I-I3 = K, [H,AsO, 1[I,- 1 was determined a t 2 5 O by direct measurement, the method employed consisting in bringing together, out of contact with the air, a standard solution of H,AsO, in water and a solution of I, in CC1,. When equilibrium was attained a sample of each liquid phase was removed and its total-iodine content determined by analysis. From these data the value of K , can be calculated with an accuracy of better than 10%. I n the seven experiments which were made in this manner the concentrations of the different molecular species taking part in the equilibrium were varied through the following concentration ranges: (I,) from 0.000007 to o.oooog or 13-fold; (I-) from 0.08 to 0.14 or nearly 2-fold; (I;) from 0.00014 to 0.011 or 80-fold; (H+) from 0.0096 to 0.16 or more than 16-fold; (H,AsO,) from 0.00025 to 0.016 or more than 60-fold; and (H,AsO,) from 0.02 to 0.086 or more than q-fold. In spite of these large variations of concentration, the value of K , was found to be constant within the experimental error, the mean for the seven experiments being 5 . 5 . 1 0 - ~with a n average deviation of only 3.5y0 and a maximum deviation of only 6y0. The apparent close adherence to the requirements of the mass-action law shown by this reaction, involving as it does three species of unionized molecules and three species of ions, the concentrations of two of the latter appearing as the second and third powers, respectively, in the equilibrium expression, contrasts strongly with the great deviation from the requirements of the mass-action law exhibited by the ionization of a strong electrolyte. 7 . I n order to understand this seemingly contradictory behavior it must be realized first of all that all the laws of dilute and of ideal solutions, including of course the law of mass action, are derived on the assumption that the “thermodynamic environment” in the solution is not a variable and none of these laws can be expected to hold if this condition is not fulfilled. 8. Aqueous solutions containing ions a t concentrations above 0.001 N do not fulfil this condition if the ion concentration is varied. As a provisional equation of state for any molecular species, A, in a solution containing ions a t the concentration C,, the following expression is suggested: I n terms of vapor pressure, .bA = k,(I ka.Cl)x,
+
and in terms of osmotic pressure z,V, = --RT log, xAk,(I
+ kiC3)
where x A is the mol fraction of A and k, an$ k i are constants characteristic of A. h is practically a universal constant and has the average value ‘1,.
714
GDWARD W. WASHBURN AND GARL$ K . S‘fRACHAN.
9. From either of these equations a complete set of laws for solutions containing ions may be derived by purely thermodynamic reasoning. The law governing the chemical equilibrium aA bB = mM nN is [MIrn [N]“ (I kiC!)(r kiC:) [A]” [Bib A? ( I kMC!)(I k$?) * which reduces to the mass-action law only when Ci is sufficiently constant or is negligibly small. IO. For the ionization of a uni-univalent electrolyte, the general expression above reduces to the form
+. ..
-..
.. ..
5=
+ +
+
+ ...
+ +
..
+
a
which is the empirical relation that Kraus and Bray have found to hold very exactly for the ionization of all electrolytes of this type. I t is evident, therefore, that a strong electrolyte can only obey the mass-action law when Ci is very small (extremely dilute solutions) or when it is kept constant (by the addition of some other electrolyte, for example). I I. For the arsenious acid-iodine equilibrium the general expression given above, assumes the form
Owing to the equality of the constants k;,, and hi,, the ratio of the two parentheses containing them is unity. Furthermore i t can be shown that the remaining parentheses in this expression reduce to ( I 4CYa). In the experiments in which the value of K,was measured Cy1 had an average value of 0.33 f 0.038, and the quantity ( I 4C:’z) becomes, therefore, becomes k,.2.3 (I 0.06), and hence may 2.3 (I f 0.06), while K , evidently be expected to show constancy within 6%. This agrees perfectly with the experimental results. The true mass law constant for this equilibrium, that is, the value approached by K, as Ci approaches zero, is the quantity k, which is approximately equal to 2.4.10-~. 1 2 . The heat of the reaction is 1360 cal. 13. The general expression for K , is log,&, = -1.3495 0.00372t. 14. The “free enefgy” of the reaction is -AFo = R T loge K, = 5690 5.42T (jou€es) for the conditions described in sec. 18. 15. The potential of the “normal” arsenic electrode is 0.293 volts under the conditions explained in sec., 19.
+
+
+
+
URBANA, ILL.
+
